Fix an \(\mathbb {F}_q\) -vector space isomorphism \(\varphi \)  between \(\mathbb {F}_{q^{k_1}}\)  and \(\mathcal {C}_{in}.\)  Define \(\mathcal {C}_{conc}\)  by
\(\mathcal {C}_{conc}=\lbrace (\varphi (c_1),\varphi (c_2),\dots ,\varphi (c_{n_2})):\; (c_1,c_2,\dots ,c_{n_2})\in \mathcal {C}_{out}\rbrace . \) 
Then \(\mathcal {C}_{conc}\)  is an \([n_1n_2,k_1k_2,\geqslant d_1d_2]_q\) -linear code from [1]}. Every position of a codeword of \(\mathcal {C}_{conc}\)  can be determined by \(r\)  other positions due to the fact that the inner code \(\mathcal {C}_{in}\)  has locality \(r\) . Hence, \(\mathcal {C}_{conc}\)  has locality \(r\) .
